On Super Magic Algorithm for Union of Comb and Star Graph

Year 2023, Volume: 11 Issue: 1, 82 - 89, 30.04.2023

Rongbing Huang Muhammad Farhan Hanif Muhammad Kamran Siddiqui Muhammad Faisal Nadeem

Abstract

In [7], Enomoto \emph{et al.} identified the concept of super edge magic total labeling of graphs by getting motivation from the idea of edge-magic labeling of graphs that was brought into light by Kotzig and Rosa [20]. An edge magic total labeling of a graph $G$ is a one to one map $\phi$ from $V(G)\cup E(G)$ onto the set $ \{1, 2, \dots , |V(G)|+|E(G)|\}$ with the property that, there is an integer constant $\alpha$ such that $\phi(u)+\phi(uv)+\phi(v)=\alpha$ for any $(u,v)\in E(G).$ Moreover if $\phi(V(G))=\{1, 2, \dots , |V(G)|\}$, then edge magic total labeling is called super edge magic total labeling. In this paper, we study the super edge magic total labeling of generalized comb graph.

Keywords

magic graph, SEM total labeling, comb graph, star

References

• [1] A. Ahmad, A. Q. Baig and M. Imran, On isuper iedge-magicness of igraphs, Utilitas Math., 2012, 89, 373-380.
• [2] M. Baca, Y. Lin, and F.A. Muntaner-Batle, Super iedge-antiimagicilabeling of path like trees, Utilitas Math, 2010, 81, 31-40.
• [3] M. Baa, M. Numan, A. Semaniov- Feovkov, Super d-antimagic labelings of generalized prism, Utilitas Math. 2016, 99, 101{119.
• [4] M. Baa, Y. Bashir, M. F. Nadeem, A. Shabbir, On super edge-antimagic total labeling of Toeplitz graphs, Springer Proceedings in Mathematics and Statistics, 2015, 98, 1{11.
• [5] M. Baa, Y. Bashir, M. F. Nadeem, A. Shabbir, On super edge-antimagicness of circulant graphs, Graphs and Combinatorics, 2015, DOI 10.1007/s00373-014-1505-2. [6] A. Q. Baig, A. Ahmad, E. T. Baskoro and R. Simanjuntak, On the isuper iedge-imagicigraphs, Utilitas Math., 2011, 86, 147-159.
• [7] H. Enomoto, A. S. Llado. T. Nakamigawa, and G.R ingle, Super iedge-imagicigraphs, SUT J.Math., 1980, 34, 105-109.
• [8] R. M. Figueroa, R. Ichishima and F. A. Muntaner-Batle, The place of isuper iedge-imagic ilabeling among other classes of ilabeling,Discrete Math. 2001, 231, 153-168.
• [9] J. A. Gallian, A dynamic survey of igraph ilabeling, Electron. J. Com-bin. 18 #DS6, http://www.icombinatorics.org/surveys/ds6.pdf (2010).
• [10] M. Hussain, E. T. Baskoro, K. Ali, On isuper antiimagicitotal ilabeling of Harary igraph, Ars icombin., 2012, 104, 225-233.
• [11] M. Hussain, E. T. Baskoro, Slamin, On isuper iedge-imagicitotal ilabeling of banana trees, Utilitas Math., 2009, 79, 243-251.
• [12] M. Javed, M. Hussain, K. Ali, K. H. Dar, On isuper iedge-imagicitotal ilabeling of w-trees, Utilitas Math., 2011, 86, 183-191.
• [13] S.R. Kim and J. Y. Park, On isuper iedge-imagicigraphs, Ars Combin., 2006, 81, 113{127.
• [14] A. Kotzig and A. Rosa, Magic valuaton of nite igraphs, Canad. Math. Bull., 1970, 13(4), 451-461.
• [15] J. Y. Park, J. H. Choi and J-H. Bae, On isuper iedge-imagicilabeling of some igraphs, Bull. Korean Math. Soc., 2008, 45, 11-21.
• [16] W. D. Wallis, Magic Graphs, Birkhauser, Boston, 2001.
• [17] W. D. Wallis, E. T. Baskoro, M. Miller, and Slamin, Edge-imagicitotal ilabelings, Australas. J. Combin., 2000, 22, 177{190.